In fibre-optic communications channels, Dense Wavelength Division Multiplexing (DWDM) is used to transmit multiple optical signals via a single fibre. For such applications, each of the channels has a distinct frequency, defined by a frequency grid (e.g. ITU-T G.694.1).
The frequencies of optical signals produced by laser sources are “locked” to the frequencies of the grid by a wavelength locking mechanism. The wavelength locking mechanism comprises a means for measuring the wavelength of each optical signal, and a feedback loop which adjusts the output of the corresponding laser source in dependence upon the measurement.
Typically, the means for measuring the wavelength comprises a Fabry-Perot (FP) etalon (or interferometer). An FP etalon is illustrated in FIG. 1A, and comprises a transparent plate with two reflecting surfaces. As the light bounces between the surfaces, the transmitted rays interfere with each other, producing a characteristic interference pattern, which is dependent upon the frequency and the optical distance between the plates.
The frequency response of a FP etalon has the characteristic curve shown in FIG. 1B. To provide the greatest resolution for the optical locker, it is calibrated such that the desired frequency is in a region of the frequency response graph with a high gradient. This means that small changes in the frequency will produce large changes in the output.
Since the behaviour of an etalon is dependent on the optical path length through the plate, the behaviour is strongly temperature dependent. The optical path will tend to increase with temperature, both due to the expansion of the material with temperature, and the change in refractive index of the material with temperature.
            P      ⁡              (        T        )              =                  n        ⁡                  (          T          )                    ⁢              L        ⁡                  (          T          )                          α    =                  1        L            ⁢                        d          ⁢                                          ⁢          L                dT                  ψ    =          dN      dT      Where P is the optical path length, n(T) is the refractive index as a function of temperature, L(T) is the physical length as a function of temperature, α is the coefficient of thermal expansion, and ψ is the thermo-optic coefficient. α is positive for most materials, ψ may be positive or negative.
Therefore, to ensure proper calibration, the temperature of an etalon must be strictly controlled. This can either be done by keeping the etalon at a constant temperature. In more sophisticated etalons such as that disclosed in WO 2015/030896, the temperature of the etalon can be varied in a controlled manner in order to allow the etalon to be automatically recalibrated to different frequencies.
The temperature control adds additional complexity and cost to the manufacture of the etalon, and so there is a need for an optical locker which can be made temperature independent.
In order to create a temperature independent etalon (to form the basis of a temperature independent optical locker), the phase difference between interfering beams must be independent of temperature. In order to achieve this, the optical path difference between the beams must be independent of temperature.
Consider a simplified FP etalon, where there are only two transmitted beams—a beam which passes straight through the transparent plate, and a beam which is reflected once off each interfering surface. P1 is the optical path length of the first beam, P2 is the optical path length of the second beam, and ΔP is the optical path difference.
      Δ    ⁢                  ⁢    P    =                    P        ⁢                                  ⁢        2            -              P        ⁢                                  ⁢        1              =                  (                              2            ⁢            π                    λ                )            ⁢      2      ⁢      nl      ⁢                          ⁢      cos      ⁢                          ⁢      φ      as can be found in any textbook discussion of the FP etalon, e.g. wikipedia.org/wiki/Fabry-Perot interferometer.
ΔP contains a contribution from the difference in path length within the transparent plate, and a contribution from the difference of path length in air. The difference of path length in air is essentially constant over reasonable temperatures, so the temperature dependence comes from the difference in path length through the transparent material. p1 is the optical path length of the first beam through the transparent material, and p2 is the optical path length of the second beam through the transparent material. Since the first and second path pass through the same material, p2=3p1, so ΔP=ΔPair+2p1. Therefore the temperature dependence of the path difference, dΔP/dT=2dp1/dT, the temperature dependence of the path through the transparent material.
dp1/dT cannot be zero for any known material. For known materials, the change in path length with temperature, dP/dT, is generally positive, as even in those materials with a negative thermo-optic coefficient, the expansion of the material itself (i.e. increase in L) counteracts the reduction in refractive index. FIG. 2 shows this—FIG. 2A shows α vs ψ for a range of glasses, and FIG. 2B shows the overall thermal path dependence for a range of glasses. Since dP/dT is positive, no combination of materials in the transparent plate can result in dp1/dT being zero.
Therefore, a temperature independent etalon is not possible.